The field of the invention is medical imaging system and methods. More particularly, the present invention relates to methods for image reconstruction that allow desirable levels of signal-to-noise ratio to be maintained while balancing other imaging considerations such as decreases in radiation dose and scan time.
In medical imaging, as well as other imaging technologies, signal-to-noise ratio (“SNR”) is utilized as a quantitative measure of image quality. Generally, SNR is defined as the ratio between the mean intensity value and the root-mean-square (“RMS”) noise, σ, in an image. The term “net signal” refers to the difference between an average signal value over the image, and background values, whereas the term RMS noise refers to the standard deviation of the noise value in the image. As SNR decreases in a medical image, it becomes increasingly more difficult to differentiate between anatomical features and other clinical findings of importance to the clinician. Thus, it is generally desirable to preserve a relatively high SNR in medical imaging applications.
In a computed tomography system, an x-ray source projects a fan-shaped beam which is collimated to lie within an x-y plane of a Cartesian coordinate system, termed the “image plane.” The x-ray beam passes through the object being imaged, such as a medical patient, and impinges upon an array of radiation detectors. The intensity of the transmitted radiation is dependent upon the attenuation of the x-ray beam by the object and each detector produces a separate electrical signal that is a measurement of the beam attenuation. The attenuation measurements from all the detectors are acquired separately to produce what is called the “transmission profile,” “attenuation profile,” or “projection.”
The source and detector array in a conventional CT system are rotated on a gantry within the imaging plane and around the object so that the angle at which the x-ray beam intersects the object constantly changes. The transmission profile from the detector array at a given angle is referred to as a “view” and a “scan” of the object comprises a set of views made at different angular orientations during one revolution of the x-ray source and detector. In a 2D scan, data is processed to construct an image that corresponds to a two dimensional slice taken through the object. The prevailing method for reconstructing an image from 2D data is referred to in the art as the filtered backprojection technique. This image reconstruction process converts the attenuation measurements acquired during a scan into integers called “CT numbers” or “Hounsfield units”, which are used to control the brightness of a corresponding pixel on a display.
Magnetic resonance imaging (“MRI”) uses the nuclear magnetic resonance (“NMR”) phenomenon to produce images. When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the nuclei in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) that is in the x-y plane and that is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped,” into the x-y plane to produce a net transverse magnetic moment Mxy. A signal is emitted by the excited nuclei or “spins,” after the excitation signal B1 is terminated, and this signal may be received and processed to form an image.
When utilizing these “MR” signals to produce images, magnetic field gradients (Gx, Gy, and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received MR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
The measurement cycle used to acquire each MR signal is performed under the direction of a pulse sequence produced by a pulse sequencer. Clinically available MRI systems store a library of such pulse sequences that can be prescribed to meet the needs of many different clinical applications. Research MRI systems include a library of clinically-proven pulse sequences and they also enable the development of new pulse sequences.
The MR signals acquired with an MRI system are signal samples of the subject of the examination in Fourier space, or what is often referred to in the art as “k-space.” Each MR measurement cycle, or pulse sequence, typically samples a portion of k-space along a sampling trajectory characteristic of that pulse sequence. Most pulse sequences sample k-space in a raster scan-like pattern sometimes referred to as a “spin-warp,” a “Fourier,” a “rectilinear,” or a “Cartesian” scan. The spin-warp scan technique employs a variable amplitude phase encoding magnetic field gradient pulse prior to the acquisition of MR spin-echo signals to phase encode spatial information in the direction of this gradient. In a two-dimensional implementation (“2DFT”), for example, spatial information is encoded in one direction by applying a phase encoding gradient, Gy, along that direction, and then a spin-echo signal is acquired in the presence of a readout magnetic field gradient, Gx, in a direction orthogonal to the phase encoding direction. The readout gradient present during the spin-echo acquisition encodes spatial information in the orthogonal direction. In a typical 2DFT pulse sequence, the magnitude of the phase encoding gradient pulse, Gy, is incremented, ΔGy, in the sequence of measurement cycles, or “views” that are acquired during the scan to produce a set of k-space MR data from which an entire image can be reconstructed.
There are many other k-space sampling patterns used by MRI systems. These include “radial”, or “projection reconstruction” scans in which k-space is sampled as a set of radial sampling trajectories extending from the center of k-space. The pulse sequences for a radial scan are characterized by the lack of a phase encoding gradient and the presence of a readout gradient that changes direction from one pulse sequence view to the next. There are also many k-space sampling methods that are closely related to the radial scan and that sample along a curved k-space sampling trajectory rather than the straight line radial trajectory.
An image is reconstructed from the acquired k-space data by transforming the k-space data set to an image space data set. There are many different methods for performing this task and the method used is often determined by the technique used to acquire the k-space data. With a Cartesian grid of k-space data that results from a 2D or 3D spin-warp acquisition, for example, the most common reconstruction method used is an inverse Fourier transformation (“2DFT” or “3DFT”) along each of the 2 or 3 axes of the data set. With a radial k-space data set and its variations, the most common reconstruction method includes “regridding” the k-space samples to create a Cartesian grid of k-space samples and then performing a 2DFT or 3DFT on the regridded k-space data set. In the alternative, a radial k-space data set can also be transformed to Radon space by performing a 1DFT of each radial projection view and then transforming the Radon space data set to image space by performing a filtered backprojection.
According to standard image reconstruction theories, in order to reconstruct an image without aliasing artifacts, the sampling rate employed to acquire image data must satisfy the so-called Nyquist criterion, which is set forth in the Nyquist-Shannon sampling theorem. Moreover, in standard image reconstruction theories, no specific prior information about the image is needed. On the other hand, when some prior information about the desired image is available and appropriately incorporated into the image reconstruction procedure, an image can be accurately reconstructed even if the Nyquist criterion is violated. For example, if one knows a desired image is circularly symmetric and spatially uniform, only one view of parallel-beam projections (i.e., one projection view) is needed to accurately reconstruct the linear attenuation coefficient of the object. As another example, if one knows that a desired image consists of only a single point, then only two orthogonal projections that intersect at the point are needed to accurately reconstruct the image point. Thus, if prior information is known about the desired image, such as if the desired image is a set of sparsely distributed points, it can be reconstructed from a set of data that was acquired in a manner that does not satisfy the Nyquist criterion. Put more generally, knowledge about the sparsity of the desired image can be employed to relax the Nyquist criterion; however, it is a nontrivial task to generalize these arguments to formulate a rigorous image reconstruction theory.
The Nyquist criterion serves as one of the paramount foundations of the field of information science. However, it also plays a pivotal role in modern medical imaging modalities such as magnetic resonance imaging (“MRI”) and x-ray computed tomography (“CT”). When the number of data samples acquired by an imaging system is less than the requirement imposed by the Nyquist criterion, artifacts appear in the reconstructed images. In general, such image artifacts include aliasing and streaking artifacts. In practice, the Nyquist criterion is often violated, whether intentionally or through unavoidable circumstances. For example, in order to shorten the data acquisition time in a time-resolved MR angiography study, undersampled projection reconstruction, or radial, acquisition methods are often intentionally introduced.
The risks associated with exposure to the ionizing radiation used in medical imaging, including x-ray computed tomography (“CT”) and nuclear myocardial perfusion imaging (“MPI”), have increasingly become a great concern in recent years as the number CT and nuclear MPI studies has dramatically increased. The reported effective radiation dose from a cardiac CT angiography session is approximately 5-20 millisievert (“mSv”) for male patients and even higher for female patients. This dose is in addition to the smaller radiation dose from the calcium scoring CT scan that is routinely performed prior to intravenous contrast injection. To perform CT-MPI as part of a comprehensive cardiac CT study would require acquiring images over the same region of the heart approximately 20-30 times, resulting in an increase in radiation dose of approximately twenty- to thirty-fold, which is an unacceptable level of radiation exposure.
When parameters of an x-ray imaging study, such as tube current and tube current time product, “mAs”, are varied in order to decrease the radiation dose imparted to the subject, the signal-to-noise ratio (“SNR”) of the resultant images suffers. For example, decreasing tube current produces a related decrease in radiation dose; however, the noise present in the resultant images is increased, thereby affecting SNR in accordance with the following relationship:
                                          S            ⁢                                                  ⁢            N            ⁢                                                  ⁢            R                    =                                    μ              σ                        ∝                          Dose                        ∝                          mAs                                      ;                            Eqn        .                                  ⁢                  (          1          )                    
where μ is the measured linear attenuation coefficient and σ is the RMS noise. Thus, if mAs is reduced by half, SNR will decrease by a factor of √{square root over (½)}, which corresponds to about a 30 percent decrease in SNR. Thus, while decreasing mAs during an x-ray imaging study provides a beneficial decrease in radiation dose imparted to the subject being imaged, the resultant images suffer from increased noise and, therefore, decreased SNR. Such images have limited clinical value.
Depending on the technique used, many MR scans currently require many minutes to acquire the necessary data used to produce medical images. The reduction of this scan time is an important consideration, since reduced scan time increases patient throughout, improves patient comfort, and improves image quality by reducing motion artifacts. Many different strategies have been developed to shorten the scan time.
One such strategy is referred to generally as “parallel MRI” (“pMRI”). Parallel MRI techniques use spatial information from arrays of radio frequency (“RF”) receiver coils to substitute for the spatial encoding that would otherwise have to be obtained in a sequential fashion using RF pulses and magnetic field gradients, such as phase and frequency encoding gradients. Each of the spatially independent receiver coils of the array carries certain spatial information and has a different spatial sensitivity profile. This information is utilized in order to achieve a complete spatial encoding of the received MR signals, for example, by combining the simultaneously acquired data received from each of the separate coils. Parallel MRI techniques allow an undersampling of k-space by reducing the number of acquired phase-encoded k-space sampling lines, while keeping the maximal extent covered in k-space fixed. The combination of the separate MR signals produced by the separate receiver coils enables a reduction of the acquisition time required for an image, in comparison to a conventional k-space data acquisition, by a factor related to the number of the receiver coils.
While the use of parallel MRI acts to decrease the amount of time required to image a subject without increasing gradient switching rates or RF power, parallel MRI methods are plagued with losses in signal-to-noise ratio (“SNR”). In general, the SNR of an image reconstructed using parallel MRI methods is decreased in accordance with the following relationship:
                                          S            ⁢                                                  ⁢            N            ⁢                                                  ⁢            R                    ∝                      1                          g              ⁢                              R                                                    ;                            Eqn        .                                  ⁢                  (          2          )                    
where g is the so-called geometry factor, or “g-factor,” and R is the acceleration factor, which describes the degree of undersampling employed and is related to, and generally limited by, the number of receiver coils in the array. Thus, parallel MRI methods suffer from a reduction in achievable SNR, offsetting the benefits provided by decreased scan time requirements.
It would therefore be desirable to provide a method for reconstructing an image of a subject from medical image data such that higher signal-to-noise ratio (“SNR”) is achievable as compared to currently available methods. It would further be desirable to provide a method for reconstructing an image of a subject in the aforementioned manner such that trade-offs between SNR and other considerations, such as radiation dose in x-ray imaging and scan time in magnetic resonance imaging, can be balanced without a significant loss in SNR.